PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

Naomi Feldheim; Ohad Feldheim; Shahaf Nitzan

doi:10.1214/20-AOP1470

PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

Naomi Feldheim^*
, Ohad Feldheim
, Shahaf Nitzan

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the persistence probability of a centered stationary Gaussian process on Z or R, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the behavior of the spectral measure of the process near zero and infinity.

Original language	English
Pages (from-to)	1067-1096
Number of pages	30
Journal	Annals of Probability
Volume	49
Issue number	3
DOIs	https://doi.org/10.1214/20-AOP1470
State	Published - May 2021

Bibliographical note

Funding Information:
Acknowledgments. N.F. acknowledges the supports of NSF postdoctoral fellowship MSPRF-1503094 held at Stanford. O.F. acknowledges the support of NSF grant DMS-1613091 while holding a postdoctoral position at Stanford. S.N. acknowledges the support of NSF Grant DMS-1600726.

Publisher Copyright:
© Institute of Mathematical Statistics, 2021

Keywords

Chebyshev polynomials
Gaussian process
gap probability
one-sided barrier
persistence
spectral measure
stationary process

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10.1214/20-AOP1470

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abstract = "We study the persistence probability of a centered stationary Gaussian process on Z or R, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the behavior of the spectral measure of the process near zero and infinity.",

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AU - Nitzan, Shahaf

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AB - We study the persistence probability of a centered stationary Gaussian process on Z or R, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the behavior of the spectral measure of the process near zero and infinity.

KW - Chebyshev polynomials

KW - Gaussian process

KW - gap probability

KW - one-sided barrier

KW - persistence

KW - spectral measure

KW - stationary process

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PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

Abstract

Bibliographical note

Keywords

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